CLASSIFICATION NOTES
No. 31.11
Strength Analysis of Liquefied Gas
Carriers with Independent Type A
Prismatic Tanks
JULY 2013
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Classification Notes
Classification Notes are publications that give practical information on classification of ships and other objects. Examples
of design solutions, calculation methods, specifications of test procedures, as well as acceptable repair methods for some
components are given as interpretations of the more general rule requirements.
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Classification Notes - No. 31.11, July 2013
Changes – Page 3
CHANGES – CURRENT
General
This is a new document.
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Contents – Page 4
CONTENTS
CHANGES – CURRENT 3
1.
1.1
1.2
1.3
General.................................................................................................................................................... 5
Introduction...............................................................................................................................................5
Objectives, Scope, and limitations............................................................................................................5
Definitions.................................................................................................................................................5
2.
2.1
2.2
2.3
2.4
Material Grade Selection ..................................................................................................................... 7
Temperature distribution and steel grade selection for hull structures .....................................................7
Material grade for cargo tanks ..................................................................................................................9
Material selection of outfitting details ....................................................................................................10
Material consideration for deck cargo tanks...........................................................................................10
3.
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Local Strength of Cargo Tanks .......................................................................................................... 11
Cargo density ..........................................................................................................................................11
Cargo tank pressure based on the IGC code ...........................................................................................11
Swash bulkhead ......................................................................................................................................12
Corrosion addition ..................................................................................................................................12
Requirements for local scantlings...........................................................................................................12
Fatigue assessment centreline longitudinal bulkhead .............................................................................12
Allowable stress for stiffeners and plates ...............................................................................................13
Deck Cargo Tanks...................................................................................................................................14
4.
4.1
4.2
4.3
4.4
4.5
Cargo Tank and Hull Finite Element Analysis ................................................................................. 15
Structural Idealization.............................................................................................................................15
Boundary Conditions ..............................................................................................................................19
Loading Conditions and Design Load Cases ..........................................................................................21
Design Application of Load Cases .........................................................................................................22
Design Criteria ........................................................................................................................................26
5.
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Local Structural Fine Mesh Analysis (ULS) ..................................................................................... 29
General....................................................................................................................................................29
Locations to be checked..........................................................................................................................29
Structural Modelling ...............................................................................................................................30
Load Cases ..............................................................................................................................................31
Application of Loads and Boundary Conditions ....................................................................................31
Acceptance Criteria.................................................................................................................................32
Structural verification for wood and dam plate ......................................................................................32
6.
6.1
6.2
6.3
Thermal Analysis of a Cargo Tank .................................................................................................... 35
General....................................................................................................................................................35
Thermal stress analysis ...........................................................................................................................35
Acceptance Criteria.................................................................................................................................35
7.
7.1
7.2
Sloshing Assessment............................................................................................................................. 36
Sloshing strength analysis.......................................................................................................................36
Liquid resonance interaction...................................................................................................................36
8.
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
Fatigue Analysis ................................................................................................................................... 37
Fatigue damage accumulation.................................................................................................................37
Fatigue Damage Evaluations ..................................................................................................................37
Locations to be checked for fatigue ........................................................................................................37
Finite Element Models............................................................................................................................38
Calculation of stress range components..................................................................................................38
Stress processing for S-N curve fatigue analysis....................................................................................39
Fatigue Strength Assessment of Hull and Cargo Tanks .........................................................................39
Fatigue assessment of cargo tank supports .............................................................................................41
9.
References............................................................................................................................................. 47
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.1 General – Page 5
1 General
1.1 Introduction
Classification Notes shall be considered in connection with DNV Rules for Classification of Ships, Pt. 3 Ch.1,
Hull Structural Design, Ships with Length 100 metres and above, /1/, and Pt.5 Ch.5, Liquefied Gas Carriers,
/2/. The aim of this Classification Note is to describe procedures for strength analysis of gas carriers with IMO
Independent Type A cargo tanks.
In general, gas carriers with IMO Independent Type A cargo tanks shall satisfy the strength criteria to main
class 1A1 as given in the Rules Pt. 3 Ch.1. Additionally, the criteria for classification notation Tanker for
Liquefied Gas as given in the Rules Pt. 5 Ch.5 shall be complied with for the inner hull, cargo tanks, and cargo
tank supports. The requirements of DNV Rules Pt. 5 Ch.5 /2/ are considered to meet the requirements of the
International Code for the Construction and Equipment of Ships Carrying Liquefied Gases in Bulk, IGC Code, /3/.
The full scope of structural analyses for type A-tanks as required by the Rules are described in this document.
However, some important exceptions can be made based on experience with conventional proven designs, and
when the cargo temperature is NOT lower than -55oC (e.g. LPG/NH3 carriers);
— Stationary and /or transient thermal analyses need normally not to be performed.
— Fatigue analysis of cargo tanks and supports is not required, Pt.5 Ch.5 Sec.5 A 1401.
The thermal analyses can be omitted subject to acceptance by the Society based on experience with similar
designs.
On the other hand, for novel designs, and/or when the cargo temperature is below -55oC
— Thermal analysis for material selection and thermal stress analysis is to be carried out, Pt.5 Ch.5 Sec.5
A900.
— Fatigue analyses of the cargo tanks and the supports shall be carried out with damage factor Cw ≤ 1.0, as
specified in Pt.3 Ch.1 Sec.16 and Classification Note No. 30.7, “Fatigue Assessment of Ship Structures”
/5/ for the hull structure.
The NAUTICUS (Newbuilding) is not a mandatory notation for Liquefied Gas Carriers, but is in many cases
specified as a voluntary notation for gas carriers with IMO Independent Type A cargo tanks.
Additional class notations as PLUS and CSA as defined in DNV rules Pt.3 Ch.1 Sec.15, may impose additional
requirements for hull and cargo tank structure to those described in this Classification Note.
Attention should be given to the additional requirements made by USCG, /4/, for vessels trading to US ports.
1.2 Objectives, Scope, and limitations
This classification note is made for design and assessment of the hull, cargo tanks and supporting structures of
gas carriers with IMO Independent Type A cargo tanks in accordance with the Rules. The objective is;
— To give a general description on material selection, and
— how to carry out relevant calculations and analyses to satisfy the rule requirements.
This Classification Note may be adapted for modification of existing carriers, subject to the limitations imposed
by the original material and fabrication techniques.
1.3 Definitions
The following SI-units (International System of units) are used in this Classification Notes:
Mass:
Length:
Time:
Force:
Acceleration:
tonnes (t)
millimetres (mm) or metres (m), stated in each case
seconds (s)
kilo-newtons (kN)
metres per second square (m/s2)
The following notations have been applied:
L
B
D
T
TM
=
=
=
=
length of the vessel in m as defined in the Rules Pt.3 Ch.1 Sec.1 B101
greatest moulded breadth in m, measured at the summer waterline
moulded depth defined as the vertical distance in m from the top of the keel to the moulded deck line
mean moulded summer draught in m, may be replaced by scantling draught TS in m (greater than
summer draught)
= minimum design draught in m amidships, normally taken as 2 + 0.02 L
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.1 General – Page 6
TMIN
F.P.
CB
go
f1
x
y
z
E
=
=
=
=
=
=
=
=
=
σ
=
τ
=
LT =
σe
=
τm
=
η
=
ηS
=
ηS+D =
ULS =
FLS =
ALS =
Min. relevant seagoing draught in m, may be taken as 0.35D if not known
forward perpendicular, see the Rules Pt.3 Ch.1 Sec.1 B101
block coefficient as defined in the Rules Pt.3 Ch.1 Sec.1 B101
standard acceleration of gravity = 9.81 m/s2
material factor depending on material strength group, see the Rules Pt.3 Ch.1 Sec.2
axis in the ship’s longitudinal direction
axis in the ship’s athwart ships direction (to port)
axis in the ship’s vertical direction (upwards)
modulus of elasticity of the steel material 2.06 · 105 N/mm2
Normal Stress
Shear Stress
material grade intended for low temperature service.
Equivalent stress as defined in Pt3.Ch.1
Mean shear stress over a net cross section
usage factor
usage factor related to static loads
usage factor related to static plus dynamic loads (ULS condition)
Ultimate Limit State; design condition related to static (S) plus dynamic (S+D), 10-8 loads
Fatigue Limit State; design condition related to repeated dynamic fatigue loads, 10-4 loads
Accident Limit State; accident design condition
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.2 Material Grade Selection – Page 7
2 Material Grade Selection
2.1 Temperature distribution and steel grade selection for hull structures
Temperature calculations of hull structure facing the cargo tanks shall be carried out. Design temperatures for
the analysis may be taken in accordance with Table 2-1.
Table 2-1 Ambient temperatures for hull temperature analyses
Still sea water
temperature,
ºC
0.0
0.0
-2.0
Regulations
Air temperature,
ºC
Speed. knots
+5.0
-18.0
-29.0
0.0
5.0
5.0
IGC code
USCG requirements, except Alaskan water
USCG requirements, Alaskan water
For ships intended for world-wide service, temperatures defined by the IGC Code may normally be used as
basis for the temperature calculations.
For ships trading to the territorial waters of the United States of America the material selection requirements
of the US Coast Guard, given in ref /4/, should be observed. These are specified in Table 2-1 for ease of
reference.
For ships intended for trade in other cold areas, other ambient temperature temperatures may be required by
port authorities or flag states.
If DAT or Winterized notation has been specified, the specified design material temperature should be used as
design ambient temperature.
For low temperature steel with design temperature below 0oC and down to -55oC, the table in DNV rules Pt.2
Ch.2 Sec.2 Table C1-3 shall be used.
Steel grade of load carrying stiffeners (e.g. deck longitudinals or bulkhead stiffeners) shall be as for the plating
for which the stiffener is attached. This also applies to structural members where direct loads are not applied.
e.g. brackets, top stiffeners, ribs, lugs attached to web frames, floors and girders.
Where liquid piping is dismantled regularly, or where liquid leakage may be anticipated, such as at shore
connections and at pump seals, protection for the hull beneath shall be provided for ships intended to carry
liquefied gases with boiling points lower than -30°C. The protecting arrangement shall consist of a liquid-tight
insulation (a wooden deck or a free, elevated drip tray), or it shall be made from a steel grade corresponding to
the requirements for secondary barriers.
The strip of deck plating between the top wing tanks in side, defined by the intersection between the deck plate
and a line at a static heel angle of ±30 degrees is regarded to be outside the secondary barrier. Steel grade “E”
may therefore be used for this deck strip.
Low temperature steel grade shall be applied to the secondary barrier and extended 500 mm (=d in Figure 2-1)
toward the centreline from the above mentioned intersection, and also to be extended 500 mm inside the top
wing tank. See Figure 2-1.
d
d
d
Non-Secondary
barrier
30
degrees
30
degrees
d
d
Equilibrium liquid O
level in hold space
d
Remark:
Low temperature steel to be applied to
secondary barrier + d of 500mm
Figure 2-1
Definition of secondary barrier
DET NORSKE VERITAS AS
Secondary
barrier
d
Classification Notes - No. 31.11, July 2013
Sec.2 Material Grade Selection – Page 8
For structural members connecting inner and outer hull, the mean temperature may be taken for selection of
steel grade.
The material grade of web frames or girders with large openings, attached to the secondary barrier, shall be the
same as the secondary barrier itself. The same apply to stiffeners attached to web frames or girders. See the
examples based on the IGC code below.
d
d
**: 1A1 requirements
##: LT grade
Secondary
Barrier
-50 0C
Secondary
Barrier
LT
0 0C
E or DH
##
0 0C
d: Extension of LT grade
-50 0C
-25 0C
E or DH
**
-50 0C
E or DH
0
-25 C
##
-25 0C
-25 0C
0 0C
0
0 C
a) Hopper tank with large opening
b) Hopper tank without large opening
Figure 2-2
Assumed temperature and steel grades for hopper tank
5 C (IGC)
5O C (IGC)
E or DH
O
**
##
-50OC
E or DH
##: LT grade
d
**: 1A1 requirements
d
d
5OC (IGC)
5O C (IGC)
E or DH
Secondary Barrier
O
-50 C
Figure 2-3
Assumed temperature and steel grades for top side tank
Engine room temperature of 5oC is normally assumed as shown below, according to the IGC code. It is assumed
that heating coil in fuel oil tank is inactive.
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.2 Material Grade Selection – Page 9
DESIGN AIR
TEMPERATURE
DECK
5OC IN GENERAL
-50O C
F.O.
TANK
ENGINE
CARGO
TANK
ROOM
INNER
BOTTOM
W. B. TK.
BOTTOM
0O C
FRAME
0 C
FRAME
O
Figure 2-4
Design temperature of engine room and fore body, IGC code
For longitudinally continuous plates extended from the secondary barrier, the plates within d = 500 mm from
the secondary barrier may be of low temperature steel grade.
Steel grade of longitudinal secondary members beyond aft most and foremost cargo tank bulkheads may be
acceptable as for 1A1 material grades.
2.2 Material grade for cargo tanks
When carbon-manganese steel is used for carriage of ammonia, cargo tanks and process pressure vessels should
be made of fine-grained steel with a specified minimum yield strength not exceeding 355 N/mm2 and with an
actual yield strength not exceeding 440 N/mm2.
Anhydrous ammonia may cause stress corrosion cracking (SSC) in containment and process systems made of
carbon and carbon manganese steels or nickel steels. In order to minimise the risk of SSC it is important that
the measures detailed in the rules Pt.5 Ch.5 Sec.15 are taken into account.
The tensile and yield properties of the weld consumable should exceed those of the tank material by the
smallest practical amount for carriage of ammonia.
d fo r d e c k p l a te
o n ly
U pper deck
L T g ra d e
LT grade
G ra d e a s p e r 1 A 1
cargo tank bulkhed
L T g ra d e fo r
s tri n g e r w e b
T o p w in g
ta n k p l a te
Aftmost or foremost
LT grade
E or D H
fo r fl a n g e
d fo r in n e r b o tto m
p l a te o n l y
E or
DH
G ra d e
as per
1A1
In n e r b o tto m
d
B or D
E or
DH
B o tto m
Figure 2-5
Selection of steel grade attached to secondary barrier
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.2 Material Grade Selection – Page 10
2.3 Material selection of outfitting details
Due considerations should be taken when selecting materials for outfitting details attached to outer hull
structures in the cargo area. Temperature in the outfitting details should be considered, due to low temperature
for the part of the outer hull that forms a secondary barrier.
Table 2-2 Steel grade for outfitting items
Outfitting item
Hatch coaming
Pad plate of pipe penetration
Pipe penetration for D ≥ 200 mm without pad plate
Pipe penetration for D < 200 mm without pad plate:
Pedestals of hose handling crane and provision cranes
Within secondary
barrier
LT
LT
LT
E
LT
Outside secondary
barrier
E
E
E
D
E
Foundations or pad plate that are made for outfitting and equipment on deck between hatch coamings outside
the secondary barrier shall have same material grade as the structure to which it is attached.
2.4 Material consideration for deck cargo tanks
Pressurized cargo deck tanks may be arranged for exchange of cargoes and cooling down of cargo tanks, i.e.
IGC tank type C.
Material grade of cargo tanks shall be selected depending on the lowest temperature of cargoes to be carried.
Especially, lowest carbon contents required by the IGC code should carefully be taken into account. The
material grade of supporting structures of deck cargo tanks attached to deck plates may be E grade, unless a
temperature analysis shows otherwise. Steel grade of doublers, foundation, fixing brackets, lifting lugs, and
access hatch may be E grade steel as well, unless a temperature analysis shows that a lower grade can be used.
Doubling plate directly contacted to deck cargo tanks should be of same material grades as that of deck tank.
Post weld heat treatment (PWHT) or mechanical stress relieving (MSR) shall be applied to deck tanks. For deck
tanks carrying ammonia, MSR is not allowed. It is noted that length of a deck tank should carefully be selected
due to limitation of available PWHT facilities. When PWHT is applied to TMCP steel, the manufacturer should
document sufficient tensile strength of TMCP steel after PWHT. Quenched & Tempered TMCP steel may be
used instead for this purpose.
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.3 Local Strength of Cargo Tanks – Page 11
3 Local Strength of Cargo Tanks
3.1 Cargo density
The cargo specific densities indicated on the specified class notations or in the relevant drawings shall be used.
If not specified in the documents, the cargo densities and design temperature in the following table may be
used.
Table 3-1 Design cargo density and temperature
Design Temp.
°C
Design
Density t/m3
Propane
Propylene
n-Butane
Vinyl Chloride Monomer (VCM)
-42.3
-47.7
-0.5
-13.9
0.59
0.61
0.60
0.97
Vapour Pressure
at 45°C,
Bar Gauge
16
20
3
5.8
Ammonia, anhydrous (NH3)
Acetaldehyde
Propylene oxide
-33.4
+20.8
+ 33.9
0.68
0.78
0.86
17
1.5
0.5
Cargo
3.2 Cargo tank pressure based on the IGC code
Cargo tank pressures according to acceleration ellipse at 10-8 probability level in DNV rules Pt. 5 Ch.5 Sec.5A
704/705/706 /2/.
The cargo pressure for a full tank is given by:
peq = po + (pgd)max.
·ρ/(1.02·104)
pgd = aαβ·Zαβ
(bar)
(bar)
where
po
(pgd)max
aαβ
ρ
Zαβ
= design vapour pressure is the maximum gauge pressure at the top of the tank, not to be taken less
than 0.25 bar. To be conservatively set to zero, P0 = 0 bar, for buckling control.
= maximum combined internal liquid pressure, resulting from combined effects of gravity and
dynamic acceleration
= the dimensionless acceleration (relative to the acceleration of gravity) resulting from gravitational
and dynamic loads, in an arbitrary direction αβ (a more detailed description is given below)
= the maximum density of the cargo in tonnes/m3 at the design temperature
= largest liquid height (m) above the point where the pressure is to be determined measured from
the tank shell in the aαβ direction (see Figure 3-1)
Zβ IV
ZβV
I
V
Zβ III
Zβ1
Zβ II
β
I
Figure 3-1
IGC pressure
DET NORSKE VERITAS AS
III
αβ
II
Classification Notes - No. 31.11, July 2013
Sec.3 Local Strength of Cargo Tanks – Page 12
The acceleration aab is calculated by combining the three component accelerations ax, ay and az values according
to an ellipsoid surface, as given in the Rules Pt.5 Ch.5 Sec.5 A704 /2/.
For different directions of aαβ in the ellipsoid, the pressure at different corner locations in the cargo tank, are
calculated according to the formula above. Based on the calculated pressures, the maximum pressures at corner
points are found. Between corner points the pressure may be found by linear interpolation. The over pressure
in tanks should normally be set to 0.25 bar in seagoing conditions.
3.3 Swash bulkhead
Swash bulkhead is normally arranged in the middle of a cargo tank to prevent sloshing impact loads to the cargo
tank. The following figure shows various swash bulkhead types due to resonance, shear stress level and
buckling.
Sloshing pressure shall be calculated according to DNV rules Pt.3 Ch.1 /1/.
C.L.
C.L.
C.L.
C.L.
Figure 3-2
Arrangement of openings of a swash bulkhead
3.4 Corrosion addition
Corrosion addition of tk = 0 mm shall be used for cargo tanks and inner side of cargo holds.
3.5 Requirements for local scantlings
The cargo tank boundary is normally constructed of plane plates supported by a system of stiffeners and
girders.
Scantlings of plates and stiffeners shall satisfy requirements of rules Pt.5 Ch.5 Sec.5 E200 /2/.
It is assumed that the top of the dome has common gas phase on both sides of the centreline liquid tight
longitudinal bulkhead. The Influence of the dome on the pressure height shall be taken into account as
described in Rules Pt.5 Ch.5 Sec.5 A706 /2/.
In seagoing conditions it is assumed that the filling height at both sides of centreline longitudinal bulkhead is
the same.
The centreline longitudinal bulkhead shall normally be designed for one side filling in harbour.
3.6 Fatigue assessment centreline longitudinal bulkhead
Upper part of liquid tight centreline longitudinal bulkhead shall be specially considered with respect to dynamic
pressures in view of fatigue. Because of the ullage effect, the cargo tank will not be 100% filled. The maximum
fill height is assumed as 98% of the tank height. The pressure amplitude for fatigue strength assessment will
be obtained from the following formula taking the effect of tank motion.
pint
 p1 = ρa v hs

3
= f a max  p 2 = ρk t at y s
4

 p3 = ρk l al x s
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.3 Local Strength of Cargo Tanks – Page 13
where
fa
h
kt
= 0.51/ h : factor to transfer the load effect from 10-8 to 10-4 probability level,
= Weibull shape parameter
= correction factor due to ullage of a cargo tank
=
kl
Btan k
H tan k
hr =
2hr
= correction factor due to ullage of a cargo tank
=
hw
Ltan k
(hs − hw + hr ) , minimum 0.0, maximum 1.0
=
=
=
=
(h
s
− hw + h p )
2h p
, minimum 0.0, maximum 1.0
the vertical distance between the top of a tank and free surface, m, = normally 0.02 H tan k
maximum cargo tank length, m
maximum cargo tank breadth, m
maximum cargo tank height, m
Btan k φ
2
Ltan k θ
2
φ=
= the maximum roll angle at 10-4 probability level, given in DNV Classification Notes 30.7 /5/,
radian
= the maximum pitch angle, at 10-4 probability level, radian given in DNV Classification Notes 30.7 /5/
θ
= the vertical distance from the point to considered to the top of a tank, m
hs
a v , at , al = ship acceleration in vertical, transverse, and longitudinal directions at 10-8 probability level,
given in DNV Classification Note 30.7 /5/ respectively.
It is noted that the internal dynamic pressure at centreline bulkhead should be double amplitude as the internal
pressures from two tanks should be taken into account. The following figure shows the internal pressure
distribution of cargo tanks.
hp =
φ
hr
hs
hw
φ
hr
pint
2pint
Linear
pressure
distribution
Figure 3-3
Internal pressure distribution due to roll of a cargo tank
3.7 Allowable stress for stiffeners and plates
Allowable stress for the tank system shall be referred to 10-8 probability level as defined in IGC /3/ and DNV
Pt.5 Ch.5 /5/.
E202: Allowable stress for secondary members (stiffeners and beams) is σB/2.66 (tensile strength) or σF/1.33
(yield strength) whichever is less to be used with the section modulus design formula.
E202: For stiffeners subject to large relative deflection (adjacent to bulkheads) allowable stress is 160f1 (S) and
215f1 (S+D).
E201: Allowable stresses of 215 f1 for plates shall only be used in relation to the plate thickness design formula.
The centreline longitudinal bulkhead is to be designed for one side static filling in harbour (S). Allowable stress
is 180 f1 N/mm2. (DNV A-tank practice)
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.3 Local Strength of Cargo Tanks – Page 14
For upper part of the centreline bulkhead, the allowable nominal stress amplitude of 120 N/mm2 shall be
satisfied for the dynamic pressure given above (at 10-4 level).
(Corresponds to (0.7 + (1 - 0.7)/0.5) × 120 = 156 ≅ 160 at 10-8 level)
For fatigue strength of longitudinals and plates in the centreline longitudinal bulkhead the allowable hot spot
stress range at 10-4 probability level is 136 N/mm2 for 108 design life cycles in North Atlantic with Weibull
slope parameter h=1 and S-N curve I (welded joint air/cathodic); Table B-1 in CN30.7 /5/.
3.8 Deck Cargo Tanks
Deck cargo tanks of type C shall be designed according to DNV rules, Pt.5 Ch.5 Sec.5 I /2/. More detailed
design guidance is given in Classification Notes No.31.13 Strength Analysis of Independent Type C Tanks /9/.
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.4 Cargo Tank and Hull Finite Element Analysis – Page 15
4 Cargo Tank and Hull Finite Element Analysis
This section gives guidance on how to perform the assessment of stresses and buckling strength in primary
support members and supports of cargo tanks and the hull surrounding the cargo tanks based on finite element
analysis.
The cargo tank and hull structures under static and dynamic hull girder bending, external and internal loads are
to be taken into consideration. Thermal stresses are to be included when relevant.
4.1 Structural Idealization
4.1.1 Coordinate system
A right-hand axis system is normally employed in the global co-ordinate system. The global X-axis is in the
ship’s longitudinal plane with its origin at the aft perpendicular, positive forward. The global Y-axis is in the
horizontal plane, positive to port, negative to starboard. The global Z-axis originated from the baseline, positive
upwards.
4.1.2 Required information for the analysis
The following information is necessary for the structural analyses:
—
—
—
—
—
general arrangement
trim and stability booklet including lightweight distribution
key plans, e.g. midship section, construction profiles and decks
cargo tanks construction drawings
cargo supports arrangement and scantlings.
4.1.3 Model extent
The FE model shall cover the full breadth of the ship in order to account for asymmetric structural layout of
the cargo tank/supporting hull structure and design load conditions (heeled or unsymmetrical loading
conditions).
Models spanning 2 + 1/2 cargo holds are recommended in order to achieve correct distribution of hull girder
bending moments and shear forces. In general, Nos.1 and 2 cargo tanks and half of No. 3 cargo tank with full
breath should be idealized. Alternatively, ½+1+½ cargo tanks amidships and No.1 cargo tank may modelled
separately.
If the geometry of the aft most hold differs significantly from the midship a separate cargo model may be
required.
4.1.4 Elements and Mesh Size
The structural assessment is to be based on linear finite element analysis of three dimensional structural models.
The general types of finite elements to be used in the finite element analysis are:
— Rod (or truss) elements are line element with axial stiffness only and constant cross sectional area along
the length of the element.
— Beam elements are line element with axial, torsional and bi-directional shear and bending stiffness and with
constant properties along the length of the element.
— Shell elements are element with in-plane stiffness and out-of-plane bending stiffness with constant
thickness.
Two node line elements and four node shell elements are, in general, considered sufficient for the
representation of both the tank structure and the hull structure. The mesh requirements given in this chapter are
based on the assumption that these elements are used in the finite element models. However, higher order
elements may also be used. In general 8 node curved rectangular and 6 node curved triangular elements will be
more stable and less sensitive to non-uniform mesh configurations.
The use of 3 node (constant stress) shell element shall be kept to a minimum. Beam elements are usually
modelled as 2 node beams.
In general, hull and cargo tank structures may be meshed with one element between stiffeners (e.g.
longitudinals) and a sufficient number of elements between stiffener supports (e.g. girders, web frames and
stringers) to maintain an aspect ratio less than 3.0. Where possible, the aspect ratio of plate elements in areas
where there are likely to be high stresses or a high stress gradient is to be kept close to one. The element mesh
should preferably represent the actual stiffening system of the structure as far as practicable so that the stresses
for the control of yield and buckling strength can be read and averaged from the results without interpolation
or extrapolation.
In special cases it may not be possible to idealize the geometry and stress distribution into suitable parts in order
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Sec.4 Cargo Tank and Hull Finite Element Analysis – Page 16
to use simplified buckling checks and/or the PULS code /6/. Typical cases may be frames and girders with free
flanges and structural parts with irregular geometry. In such cases a FE buckling calculation may need to be
carried out of those areas. This can be done as a sub-model with a mesh designed to capture the dominating
buckling modes.
When using non-linear FE programmes like ABAQUS special considerations with respect to modelling (mesh
fineness), imperfection levels, imperfection modes and acceptance levels is required and will be considered by
the Society.
Elastic buckling of plates and stiffeners in the cargo tanks shall not be allowed as frequently occurring elastic
buckling of plates will increase the probability of crack initiation along plate boundaries.
Hence, with PULS use analysis option BS, Buckling Strength, for tank and associated support structures.
Use analysis option UC, Ultimate Capacity, for the hull structures in general.
The UC option allows for elastic buckling for slender structures which shall not be allowed for the tank
structure
For definition of average stress and selection of suitable buckling panels (equivalent plate panels-EPP) see Ch.8
Sec.3 in the harmonized CSR-H rules, ref. /10/.
4.1.5 Modelling of geometry
All the structurally material of the hull structure shall be modelled. Plating members such as deck, bottom,
inner bottom, side shell, transverse webs, watertight bulkheads, cargo tank bulkheads and shell, stringers, etc.
shall be modelled by shell elements.
The stiffeners subjected to lateral pressure, e.g. longitudinal stiffeners and vertical stiffeners attached to cargo
tank bulkheads shall be represented by beam elements. Face plates of primary supporting members as deck
transverse webs and face plates of cargo tank horizontal stringers may be represented by beam or truss elements
in order to represent bending properties properly. Secondary structural members, such as buckling stiffeners
on transverse webs, girders/stringers, etc. may be modelled by truss elements.
Small openings in double bottom floors/girders and web frames and bulkheads of cargo tank may be not
modelled. Openings in way of critical areas shall be specially evaluated after opening area reduction with
regard to shear strength. Modelling is to be according to the procedure in Classification Notes 31.3.
All hull structures shall be modelled based on gross scantlings minus the corrosion allowance tk (modelled
scantlings) as given in the rules.
Cargo tank supports may be modelled by using shell elements. An iterative procedure may be required to
eliminate elements under tensile loads.
4.1.6 Modelling of supports
Vertical supports, anti-rolling/pitching supports and anti-floating supports may be idealized by shell elements.
The supports on hull and cargo tank may be interconnected with solid elements or beam/truss elements
representing the support blocks. If linear elements are employed, the connection elements shall be disconnected
when they are in tension (i.e. no contact). An iterative procedure may be required; supports in tension shall be
disconnected and the FE model rerun until all active supports are in compression.
The cargo tanks are supported by the following supports.
—
—
—
—
Vertical supports in global Z direction
Anti-rolling keys in global Y direction
Anti-pitch anti-collision keys in global X direction
Anti-flotation keys global in global Z direction.
Unless otherwise documented by the designer, friction coefficients to use with the analyses of the supports are
shown in Table 4-1.
Table 4-1 Friction coefficients (guidance values)
Surface
Material
1
Surface
Material
2
Static friction
coefficient,
Dynamic friction
coefficient,
Steel
Steel
Wood
Synthetic Resin
0.5
0.5
0.2
0.2
Steel
Steel
0.17
0.15
µs
µd
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Anti-floating
support , if applied
Vertical
supports
Upper anti roll supports
Lower anti -roll
supports
Figure 4-1
Location of cargo tank supports (example)
4.1.7 Analysis strategy for ULS assessment
4.1.7.1 Vertical Supports
Various types of vertical supports are used. The following figure shows an example of a vertical supports.
Normally Wood mounted on resin will contribute to levelling of vertical supports in a cargo hold. Dam plates
are fitted to avoid movement of wood in case of damages in resin or bond between resin and top plate of a
vertical support.
Figure 4-2
Example of modelling of a vertical support
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The support chocks can be modelled in several ways; either by solid elements combined with contact elements
or modelled as beams with representative axial and shear stiffness. It is important that the model correctly
remove the vertical load on supports in tension. This means that beams/contact elements in tension are removed
(the vertical stiffness set to zero or a very small value) and the analysis repeated until all active vertical supports
are in compression.
If it is seen that the combined longitudinal and transverse force exceeds the static friction force limit, the shear
stiffness has to be removed for the connection elements and the calculation rerun with no shear coupling. The
friction force acting on the interfacing surfaces must be applied to both parts of the supports with a magnitude
of the static friction coefficient (µS) times the vertical force acting on each individual support. The static friction
coefficient can, if not otherwise specified by the designer, be conservatively set to 0.5, Table 4-1.
Figure 4-3
Modelling of anti-roll and anti-pitch supports
4.1.7.2 Transverse anti-roll supports
The anti-roll supports are designed based on the transverse acceleration load cases (LC 6 and 7) and the heeled
load cases (LC8-9). In these load cases some of the transverse force is carried by friction in the vertical supports
and the rest is taken by the upper and lower anti roll supports.
In order to be able to predict the distribution of forces between the upper and lower anti-roll supports a refined
cargo hold analysis procedure should be used. This is based on an iterative approach.
1) All vertical supports are initially modelled with actual shear and bending stiffness.
2) The transverse forces in each of the supports are calculated.
3) If the dynamic friction force of a vertical support is exceeded, the shear and bending stiffness of the support
is set to zero and the dynamic friction force is applied as a force couple.
4) The analysis shall be repeated to determine the new distribution of horizontal support forces.
This procedure shall be repeated until all the transverse support forces are less or equal to the dynamic friction
force.
The dynamic friction force is calculated as the dynamic friction coefficient (µd) times the vertical force acting
on each individual support. If not otherwise documented by the maker of the wood blocks, a dynamic friction
coefficient of 0.2 can be applied, Table 4-1.
Effects of intentional clearances between support surfaces should be include if this is expected to significantly
affect the distribution of forces between the upper and the lower roll supports.
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Figure 4-4
Example of anti-pitch support
4.1.7.3 Longitudinal anti-pitch supports
The ULS assessment of the anti-pitch supports is based on the collision load cases (LC10 and 11). Normally
LC 10 will be governing. As for the anti-roll supports, some of the load in longitudinal direction will be taken
by the friction in vertical supports and the rest will be taken by the anti-pitch supports.
The same iterative approach as described in the previous section should be utilized. If sliding occurs (the
longitudinal force exceeds the static friction force), the analysis should be rerun with applied dynamic friction
forces. Then it is possible to obtain the distribution of forces between outer and inner anti-pitch supports.
Figure 4-5
Example of an anti-floatation support
4.1.7.4 Anti-floatation supports
These supports are analysed similarly as the vertical supports. Deformations of the local models are taken from
the cargo hold model analysed with the flooding condition (LC 12). The friction forces are to be calculated as
described in [4.1.7.1], but the direction of these forces should be found from the cargo hold analysis.
4.2 Boundary Conditions
The boundary conditions for applying bending moments are shown in Figure 4-6. Load cases applying pressure
are shown in Figure 4-7.
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Shear force along side shell to
obtain the traget bending moment
at the considered section
For longitudinal members
of hull and cargo tank
Symmetric B.C.
dx = dz = Rx = Ry = 0
No.1 tank
No.2 tank
No.3 tank
Collision
Trans. bulkhead
bulkhead
Note:
dy = 0
Z
Y
Shear force shall be applied at
transverse bulkhead to achieve the
target bending moment at the section
to be checked
X
Figure 4-6
Boundary condition, bending moments are applied
For longitudinal members
of hull and cargo tank
Symmetric B.C.
Vertical springs at
dx = Rx = Ry = 0
W.T. transverse
bulkhead
Vertical springs at
W.T. transverse
bulkhead
Vertical springs at
W.T. transverse
bulkhead
No.1 tank
No.2 tank
No.3 tank
Collision
bulkhead
dy = 0 at centre
line of W. T.
bulkhead
Z
Y
X
dy = 0 at centre
line of W. T.
bulkhead
Note:
dy = 0 at
horizontal line of
W. T. bulkhead
Reaction forces may be applied
instead of vertical springs
Figure 4-7
Boundary condition, symmetric pressure is applied
For asymmetric load case, the following figure shows boundary conditions.
For longitudinal members
of hull and cargo tank
Symmetric B.C.
Vertical springs at
dx = R x = R y = 0
W.T. transverse
bulkhead
Vertical springs at
W.T. transverse
bulkhead
Vertical springs at
W.T. transverse
bulkhead
No.1 tank
No.2 tank
No.3 tank
Collision
bulkhead
dy = 0 at
horizontal line of
W. T. bulkhead
Y
Z
X
dy = 0 at
horizontal line of
W. T. bulkhead
Note:
dy = 0 at
horizontal line of
W. T. bulkhead
Reaction forces may be applied
instead of vertical springs
Figure 4-8
Boundary condition, asymmetric pressure is applied
Weight of cargo tanks, support blocks and hull structures shall be taken into account.
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Sec.4 Cargo Tank and Hull Finite Element Analysis – Page 21
Reaction forces or springs to be applied to the transverse bulkheads to counteract for the imbalance of vertical
forces. In addition, transverse horizontal constraint should be added to a node at the intersection between the
transverse bulkhead and bottom/deck. Transverse directional spring elements are recommended for both ends
of model instead of fix condition (dy = 0). Spring constants may be estimated as shown in CN 30.3 ignoring
the effect of bending deflection.
For application of bending moment at both ends of model, nodal points of all longitudinal elements should be
rigidly linked (dx, Ry and Rz) to independent node (Master node) at neutral axis on centre line. This ensures
the intersection plane to be planar. The longitudinal translation of master node of one end of the model needs
to be fixed
Bending moment and shear force adjustment should be carried out to get target global bending moment and
shear force.
The vertical hull girder bending moment shall be applied to achieve the target value at the location to be
checked in the model. Some modifications to the size of this bending moment is necessary. The background
for this is that the acceptance criteria for hull girder stress are based on gross scantlings. The modelled
scantlings in the FEM model are based on gross scantling reduced by tk. It is therefore necessary to reduce the
Hull girder bending moment by a factor of Zmod / Zgross. Zmod is the hull girder section modulus as modelled (i.e
gross scantling reduced by the corrosion addition, tk) and Zgross, the hull girder section modulus based on actual
(as built) scantlings. As the bottom area is critical due to buckling, the hull girder bending stress correction may
normally be made by using the section modulus at bottom.
4.3 Loading Conditions and Design Load Cases
The design load cases are selected based on actual loading conditions from vessel’s loading manual. Therefore,
all possible conditions such as seagoing, harbour and damaged condition are to be included into the loading
manual.
The design load conditions should include fully loaded condition, alternate conditions (realistic combinations
of full and empty cargo tanks) with static(S) and static and dynamic (S+D) sea pressure/tank pressure, giving
maximum net loads on double bottom structures.
The basis for the selection of load conditions is to maximize the cargo tank and hull stress response by
combining internal and external loads with hull girder bending.
Design loads including actual bending moments and maximum cargo accelerations and sea pressure, are
applied to the global cargo hold finite element model. The loads are calculated for a 20 year return period for
the North Atlantic and serve as basis for design against yield and buckling strength of cargo tanks, the supports,
the supporting double bottom structures and the hull structure. Note that the worst combination of loads shall
be considered. In some cases this may result in removing loads (shall be realistic) to archive the largest stresses
for particular elements.
Table 4-2 and Table 4-3 list applicable design loading conditions for analysis of amid-ship cargo areas given
in the Rules Pt.5 Ch.5 Sec.5 /2/. The tables include an indication of the applicable structural part and analysis.
These design load cases are based on relevant loading conditions for independent tank type A, constructed
mainly of plane surfaces. The loading manual may specify loading conditions with respect to allowable drafts
and ballast conditions of ballast water for the vessel in question.
Some load cases given in Table 4-2 may be omitted in the analysis considering actual hull girder bending
moment and its effect on the vertical supports.
Dynamic sea pressure shall be calculated from one of the following rules, depending on the probability level
employed.
— Pt.3 Ch.1 Sec.4 C200, referring to probability level of 10-4
— Pt.5 Ch.5 Sec.5 E303, referring to probability level of 10-8
Cargo loads, static (S) and dynamic (D) loads shall be calculated, depending on the probability level employed.
Cargo tank pressures:
Static pressure (S):
Psta. = ρc g hz + P0
Vertical pressure (S+D):
Pdyn = ρc g (1 + az) hz + P0
: at 10-8 level
Pdyn = ρc g (1 + 0.5az) hz + P0 : at 10-4 level
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Sec.4 Cargo Tank and Hull Finite Element Analysis – Page 22
Transverse pressure (S+D):
Pdyn. = (ρc g hz + P0) + ρc g hy ay : at 10-8 level
Pdyn. = (ρc g hz + P0) + 0.5ρc g hy ay : at 10-4
Pressure for ballast tanks:
Static pressure (S)
Psta.= ρw g hz
Vertical pressure (S+D):
Pdyn.= ρw g (1 + az) hz
: at 10-8 level
Pdyn = ρw g (1 + 0.5az) hz : at 10-4 level
where:
ρc
ρw
g
Po
design density of cargo in t/m3, Table 3-1
design density of ballast water, 1.025 t/m3
gravity, 9.81 m/s2
design vapour pressure at seagoing condition, subject to special consideration.
A vapour pressure higher than Po may be accepted in harbour condition where dynamic loads are
reduced.
hy, hz = local head for pressure measured from the tank reference point in the transverse and vertical direction,
respectively
ay, az = maximum dimensionless acceleration (relative to the acceleration of gravity) at the centre of gravity
of the tank in the transverse and vertical direction, respectively
=
=
=
=
The weight of a cargo tank and hull structures is to be included in the FE analysis.
For buckling control the cargo vapour pressure shall be taken equal to zero, Po = 0 bar.
4.4 Design Application of Load Cases
Primary members shall mainly be governed by one or several loading conditions. These are summarized in, but
not limited to, the Load Cases in Table 4-2 and Table 4-3.
Table 4-3 gives indications on which Load Cases will influence on the design of the various areas in the tank
and hull structure. However, other areas (members) not mentioned may need to be reviewed with additional
relevant load cases.
The transverse acceleration load cases (LC 6 and 7) and the heeled load cases (LC 8 and 9) are used to verify the
keying arrangement, cargo tank web frame structure and hopper frames. A heeling angle of 30° shall be used as
specified in Pt.5 Ch.5 Sec.5 A1104 and the IGC code. The internal pressure in the cargo tank shall be based on the
combined effect of gravity go and a transverse acceleration component of gravity amounting to ay= go sin(30) = 0.5go.
For Load Case 16, the double side ballast tank and the cargo hold is assumed punctured with water ingress into
the hold space between the hull and the cargo tank. The maximum static pressure from the inclined damaged
waterline is to be applied to the transverse bulkhead. It is to be ensured that the cargo tank is intact and no cargo
leakage into the cargo hold (void space) takes place.
The Load Cases and Loading Conditions shown in Table 4-2 and Table 4-3 shall be applied for evaluation of
Tank 2. Similar load cases need to be applied for other tanks
It should be noted that the loading conditions given in Table 4-2 and Table 4-3 are minimum loading
conditions. If more severe loading conditions, e.g. two adjacent cargo tanks empty or full, etc. are given in the
loading manual, these conditions shall also be taken into account.
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Table 4-2 Load Cases for Tank, Hull and Tank Supporting Structures
Load
Case
Loading
condition
Tank
load
Sea
press. Draugth
Illustration
TS
— Still water bending moment MS:
max. hogging bending moment
from Trim and Stability (T&S)
booklet: All tanks full or any one
tank empty others full.
MS ≥ 0.5 MS_rule hogging.
— Wave bending moment: MW = 0
TMIN
— Still water bending moment MS:
max. sagging bending moment
from T&S booklet. Alternate tank
filling or any one tank full others
empty.
MS ≥ 0.5 MS_rule sagging
— Wave bending moment: MW = 0
TS
— Still water bending moment
MS = LC 1 (hogging):
— Wave bending moment:
MW = 1.0 MW_rule hogging
— Vertical acceleration (az) of a cargo
tank combined with gravity, (go).
TMIN
— Still water bending moment
MS = LC 2 (sagging):
— Wave bending moment:
Mw = 1.0 Mw_rule sagging
— Vertical acceleration (az) of cargo
tank combined with gravity, (go).
TS
— Still water bending moment
MS = LC 1 (hogging)
— Wave bending moment:
MW = 1.0 MW_rule hogging
— Max. dynamic sea pressure Pt.5
Ch.5 Sec. 5.
TS
— Still water bending moment
MS = LC 1 (hogging):
— Wave bending moment:
MW = 0
— Transverse acceleration (ay) of
cargo tank combined with gravity
(go).
TMIN
— Still water bending moment
MS = LC 2 (sagging):
— Wave bending moment:
MW = 0
— Transverse rule acceleration (ay) of
cargo tank combined with gravity
(go)
Full load
LC 1
Hogging
S
S
Static (S)
Alternate
loading
LC 2
Sagging
S
S
Static (S)
LC 3
Head
Sea
(ULS)
LC 4
Head
Sea
(ULS)
LC 5
Head
Sea
Full load
Seagoing
Alternate
load
Seagoing
Sagging
(S+D)
S+D
(10-8)
LC 6
Full load
Seagoing
Beam
Sea
Max ay
(ULS)
Dynamic
condition
(S+D)
LC 7
Alternate
load
Seagoing
Max ay
S
S+D
S
(ULS)
(ULS)
(10-8)
Full load
seagoing
Hogging
(S+D)
Beam
Sea
S+D
S
Hogging
(S+D)
(10-8)
S+D
(10-8)
S
S+D
S
(10-8)
Comments
Dynamic
(S+D)
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Table 4-2 Load Cases for Tank, Hull and Tank Supporting Structures (Continued)
Load
Case
LC 8
Loading
condition
Full load
Heeled
condition
Tank
load
S
Sea
press. Draugth
S
(ULS)
Illustration
TS
— Still water bending moment
MS = LC 1 (hogging):
— Wave bending moment: MW = 0
— Inclination 30o with static sea
pressure from Pt.5 Ch5. Sec.5 (Pt.3
Ch.1)
TMIN
— Still water bending moment
MS = LC 2 (sagging):
— Wave bending moment: MW = 0
— Inclination 30o with static sea
pressure from Pt.5 Ch5. Sec.5 (Pt.3
Ch.1)
TS
— Still water bending moment
MS = LC 1 (hogging):
— Wave bending moment: MW = 0
— Acceleration ax = 0.5 go forward
combined with gravity (go)
TS
— Still water bending moment Ms =
LC 1 (hogging):
— Wave bending moment: Mw = 0
— Acceleration ax = 0.25 go aftward
combined with gravity (go)
— LC 10 will normally be governing
TS
— Maximum still water hogging
bending moment Ms from T&S
booklet (one tank empty):
MS ≥ 0.5 MS_rule hogging.
— Wave bending moment:
MW = 0.67 MW_hogging in
World-Wide environment,
Mw-ww = 0.8 Mw-NA
— Use full draught (Ts) to maximise
upward force (anti flotation keys)
0.5TS
— Still water bending moment:
MS = 0
— Wave bending moment: MW = 0
— Vapour pressure (Po) in harbour
condition to be added in loaded and
empty holds.
Static (S)
Alternate
load
LC 9
(ULS)
Heeled
condition
S
S
Static (S)
Full load
LC10
(ALS)
Collision
ax=0.5go
forward
S+D
S
Full load
LC11
(ALS)
Collision
ax=0.25go
aftwards
S+D
S
LC12
Head
Sea
Flooded
one hold
empty
S
S
(ALS)
LC13
(ULS)
Cargo tank
centreline
bulkhead
S
S
Comments
Harbour
Static (S)
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Table 4-2 Load Cases for Tank, Hull and Tank Supporting Structures (Continued)
Load
Case
Loading
condition
Tank
load
Sea
press. Draugth
Illustration
Full load,
hull design
LC14
(ULS)
Seagoing
Hogging
— Still water bending moment
MS = LC 1 (hogging):
— Wave bending moment:
MW = 0.59 MW_rule hogging
S+D
S
(10-4)
TS
This condition will in most cases be
overruled by LC 5 at 10-8 level.
Dynamic
(S+D)
LC15
(ULS)
Alternate
load, hull
design
seagoing
Hogging
TMAX
— Maximum still water hogging
bending moment Ms from T&S
booklet, alternate condition or one
tank empty others full:
— MS ≥ 0.5 MS_rule hogging.
— Wave bending moment:
MW = 0.59 MW_rule hogging
TDAM
— Still water bending moment MS = 0
— Wave bending moment: MW = 0
— Heeled damage waterline to be
applied to the transverse bulkhead.
The vertical distance shall not be
less than up to the bulkhead deck.
— Primary tank structure to be intact
and no leakage from tank.
S+D
S
(10-4)
Dynamic
(S+D)
LC16
(ALS)
Damaged
condition
S
Comments
Note:
1) TS : scantling draught
TMIN : actual minimum draught at any hold loaded condition
TMAX: actual maximum draught at any hold empty condition
TDAM: damaged draught from damage stability calculation
2) The design conditions given in Table 4-2 assume that the ballast tank under a loaded cargo tank is empty, and the
ballast tank under an empty cargo tank is full. If the actual conditions in the loading manual include more severe
assumption than above, the actual condition of the ballast tank shall be applied.
3) The design loading conditions given in Table 4-2 and 4-3 are valid for homogeneous and alternate loading of the
vessel. However special loading conditions as shown below should be considered for the evaluation of transverse
hull bulkhead, if applicable, based on vessel’s loading manual.
- Tank nos. 1 and 4 full, tank 2 and 3 empty
- Tank nos. 1 and 4 empty, tank 2 and 3 full
When these loading conditions are applied, all of the cargo tanks in the analysis should be empty and full with
maximum actual draft and minimum actual draft, respectively.
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Table 4-3 Design application of Loading Conditions and Load Cases
Loading conditions
Load Cases
Seagoing hogging condition, all tanks
full, draught TS:
LC 1 Static hogging
LC 3 Dynamic seagoing hogging
LC 5 Dynamic seagoing hogging
LC 6 Max. transverse acceleration
LC 8 Static 30o heeled condition
LC 10 Collision ax = 0.5 g0 forward
LC 11 Collision ax = 0.25 g0 aftward
LC 14 Hull design case
Seagoing hogging condition, alternate
filling or one tank empty others full,
draught TS:
LC 1, 3, 5, 6, 8, 10, 11, 14 also to be
checked for this loading condition.
LC 12 Flooded condition, one hold empty
hogging
LC 15 Hull design, draught TMIN
Comments/Application
Cargo tanks and support system, 10-8:
Double bottom structure, cargo tank
and vertical supports,
LC 1, 2, 3, 4, 5
Double bottom, deck structure, cargo
tank, vertical and
— transverse supports,
LC 6, 7, 8, 9, and
— longitudinal supports LC 10, 11.
— Keying arrangement and support
structure, LC 8 and 9
Tank, anti-floatation supports,
keying arrangement and support
structure: LC 12
-4
Seagoing sagging condition, alternate or Hull structure, 10 :
one tank full others empty, draught TMIN: Deck and double side structure, LC 14
Double bottom and side, LC 15
LC 2 Static sagging
LC 4 Dynamic seagoing sagging
LC 7 Max. transverse acceleration
LC 9 Static 30o heeled condition
Asymmetric tank filling harbour.
LC 13, draught 0.5 TS
Cargo tanks:
Strength of tank centreline bulkhead.
Static damaged condition:
LC 16, draught TDAM
— Heeled damage waterline to be
Hull structure:
applied to the transverse bulkhead.
Strength of transverse cargo hold
The vertical distance shall not be less bulkhead in damaged condition.
than up to the bulkhead deck
— Primary tank structure to be intact
and no leakage from tank.
4.5 Design Criteria
4.5.1 General
The corresponding strength criteria for each load case are summarized in Table 4-3. Scantlings of the transverse
and longitudinal primary cargo tank structures shall be determined according to the following yielding and
buckling criteria of DNV rules reflecting the IGC codes.
The strength criteria to be used for evaluation of hull structures supporting a full cargo tank, probability level
Q=10-8, are described in the Rule Pt.5 Ch.5 Sec.5.
The strength criteria to be used for evaluation of hull structures supporting an empty tank, probability level
Q=10-4, the corresponding strength criteria described in the Rule Pt.3 Ch.1 Sec.12 and 13 shall be used.
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.4 Cargo Tank and Hull Finite Element Analysis – Page 27
It is noted that the stiffener bending stress is not a part of the girder bending stresses. The magnitude of the
stiffener bending stress included in the stress results depends on the mesh division and the element type that is
used.
The mean shear stress, τmean, is to be used for the capacity check of a plate. This may be defined as the shear
force divided on the effective shear area. For results from finite element methods the mean shear stress may be
taken as the average shear stress in elements located within the actual plate field, and corrected with a factor
describing the actual shear area compared to the modelled shear area when this is relevant. For a plate field
with n elements the following apply:
i =n
τ mean =
∑ (τ . A )
i =1
i =n
i
i
∑A
i =1
i
where
Ai = the effective shear area of element i.
= the shear stress of element i.
Aw = effective shear area according to the Rules Pt.3 Ch.1 Sec.3.
τi
4.5.2 Allowable yielding and buckling criteria
The criteria shall be applied as defined in Table 4-4 for tanks with supporting structure and the hull structure.
In cases where the acceptance criteria are referring to equivalent stress no separate requirement to shear stress
is given as shear is already included in the equivalent stress concept.
DET NORSKE VERITAS AS
Table 4-4 Acceptance Criteria for Cargo Hold Analysis of Tanks, Supports and Hull
Directional
stress
Equivalent stress
Load Case
Hull structures
Supporting cargo
tanks 1)
Pt.3 Ch.1 Sec.13
-
0.6
-
-
-
0.9 to 1.0
0.85
-
215f1 / 225f1
-
-
0.9 to 1.0
0.85
-
215f1 / 225f1
215f1 / 225f1
-
-
0.9 to 1.0
0.85
-
S+D
225f1 / 235f1
225f1 / 235f1
-
-
0.9 to 1.0
1.0
-
S+D
225f1 / 235f1
225f1 / 235f1
-
-
0.9 to 1.0
1.0
-
S
-
180f1
-
-
0.7 to 0.8
0.7
-
S
-
160f1
-
-
0.6 to 0.7
0.6
-
S+D
-
-
160f1/190f1
90f1/100f1 4)
-
-
1A1 req.
-
220f1
120 f1
0.7 to 1.0
1.0
1.0 5)
S
150f1 /160f1
-
S+D
215f1 / 225f1
215f1 / 225f1
S+D
215f1 / 225f1
S
LC1-LC2
hog. & sag.
ULS
(hog. and sag.)
ULS (ay & g0)
ULS
(Heel 30o)
ALS (Collision
ax=0.5g0/0.25g0)
ALS
(Anti-flotation)
ULS
(Internal struct.)
ULS
(Str. attached to
primary barrier)
ULS (hog.)
ALS
(Dam. Flooding)
LC10-11
LC12
LC13
LC14-15
LC16
S
225f1 / 235f1
5)
Pt.3 Ch.1 Sec.12, Table B1
1)
A/B: A is without hull girder loads / B is with hull girder loads included
2)
When USCG requirements are applied, allowable stress shall be specially considered.
3)
For buckling control the vapour pressure shall be taken as zero, Po = 0 MPA, and lateral pressure shall be included as relevant.
4)
If two plate flanges, ref. Pt.3 Ch.1 Sec.12 Table B1.
5)
For transverse cargo hold bulkheads
General comments:
a)
Due to the seriousness of tank and tank support system failure the usage factors for static (S) and static plus dynamic (S+D) conditions has been reduced as compared to the values of 0.8 and 1.0 commonly applied for hull
structures in general.
b)
When using PULS use;
- analysis option BS, Buckling Strength, for buckling control of primary support members and associated tank support structure.
- the UC option, Ultimate Capacity, for hull structures in general.
Classification Notes - No. 31.11, July 2013
NOTE:
For an independent type A-tank the acceptance criteria for the tank, the attached supports and the supporting hull structure are essentially the same, Pt.5 Ch.5 Sec.5 E (10-8 level)
Sec.4 Cargo Tank and Hull Finite Element Analysis – Page 28
DET NORSKE VERITAS AS
η for PULS
Loads
LC8-LC9
Hull
structures
Pt.5 Ch.5 Sec.5
E 308
0.6 to 0.7
Rem.
LC6-LC7
Buckling Criteria
Cargo tanks, hull structures
and supports attached
to cargo tanks3)
Hull
Structures
Pt.5 Ch.5 Sec.5
E300
150f1 /160f1
LC no
LC3-LC5
Cargo tanks and
supporting structure
attached to cargo
tanks2)
Mean shear
stress
Classification Notes - No. 31.11, July 2013
Sec.5 Local Structural Fine Mesh Analysis (ULS) – Page 29
5 Local Structural Fine Mesh Analysis (ULS)
5.1 General
Local structural analyses are to be carried out to analyse stresses in local areas where high reaction forces are
found on cargo tanks, the tanks supports and supporting hull structures. Stresses in laterally loaded local plate
and stiffeners may need to be investigated. Further, stiffeners subjected to large relative deformations between
girders or frames and bulkhead shall be investigated along with stress increase in critical areas such as brackets
with continuous flanges and the cargo tanks in way of supports.
5.2 Locations to be checked
The following areas shown in Table 5-1 in the midship cargo region is a list of details to be investigated with
fine mesh analysis. The need for fine mesh analysis of these areas may be determined based on a screening of
the actual geometry and the results from the cargo hold analysis. Additional locations may also be required to
be analysed based on the outcome of the screening.
Table 5-1 Standard locations required for fine mesh analysis
Locations to check
Applied loads
— Maximum reaction force from cargo hold analysis (LC 1, 2, 3, 4, 5) in
Vertical supports
Sec.4 to be combined with horizontal friction force.
- Vertical reaction force + horizontal transverse friction force
Bracket ends in way of
high stressed areas
- Vertical reaction force + horizontal longitudinal friction force
— Static friction coefficient (before sliding) of min. 0.5 to be used if not
High stressed tank strucotherwise documented by the designer
ture in way of supports
— Each representative design to be assessed
— Maximum reaction force from cargo hold analysis (LC 6, 7, 8, 9) in Sec.
4 to be applied.
Upper & lower transverse — For lower transverse supports, total transverse dynamic (when sliding)
Cargo tanks support
friction force due to vertical supports to be deducted and not to be taken
and Tank supgreater than 0.2 of total weight of the cargo and cargo tank
ports
— Each representative design to be assessed
— Maximum reaction force from cargo hold analysis (LC10 and 11) in
Sec.4 to be applied.
Upper and lower
— For lower longitudinal supports, total longitudinal friction force due to
longitudinal support
vertical supports to be deducted and not to be taken greater than 0.2 of
total weight of the cargo and cargo tank
— Each representative design to be assessed.
— Reaction force from cargo hold analysis (LC 12) in Sec.4 to be applied.
Anti-floatation supports — Each representative design to be assessed.
Fwd and aft end second- — Maximum reaction force from cargo hold analysis in Sec.4 to be
ary stiffener structures
combined with horizontal friction force, see Figure 5-2.
— Internal inertia pressure due to:
- vertical acceleration
- transverse acceleration
Cargo tank
and tower supports
pump tower Tower
- longitudinal acceleration.
Tank dome connection
(if used)
— Sloshing forces
— General information on pump tower loads are given in Classification
Notes 30.9 Sec.4.
Hopper knuckles and
— Cargo tank full + min. Draft, LC2 in Table 4-2 and Table 4-3
Hull strucstiffeners with brackets
— Cargo tank full + min. Draft, LC4 in Table 4-2 and Table 4-3
tures
subjected to large defor- — Cargo tank empty + max. draft, LC15 in Table 4-2 and Table 4-3
mations
— Ref. also Nauticus (Newbuilding) requirements
Side hold hull Top and bottom of side
— Sea pressure loads combined with cargo and ballast loads
frames
hold frame ends
Transverse
Vertical stiffeners to inner — Relative deflection due to cargo loads
Bulkheads
bottom
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.5 Local Structural Fine Mesh Analysis (ULS) – Page 30
Figure 5-1
Critical areas for fine mesh analysis in way of double bottom structure
5.3 Structural Modelling
The fine mesh analysis shall be carried out by means of a separate local finite element model with fine mesh
zones, in conjunction with the boundary conditions obtained from the cargo tank model, or by incorporating
fine mesh zones into the cargo tank model.
The extent of the local finite element models is to be such that the calculated stresses at the areas of interest are
not significantly affected by the imposed boundary conditions and application of loads. The boundary of the
fine mesh model is to coincide with primary support members, such as girders, stringers and floors, in the cargo
tank model.
The fine mesh zone shall represent the geometry of the localised area with high stress. The finite element mesh
size within the fine mesh zones is not to be greater than 50 mm × 50 mm. In general, the extent of the fine mesh
zone is not to be less than 10 elements in all directions from the area under investigation.
All plating within the fine mesh zone is to be represented by shell elements. A smooth transition of mesh
density is to be maintained. The aspect ratio of elements within the fine mesh zone is to be kept as close to 1:1
as possible. Variation of mesh density within the fine mesh zone and the use of triangular elements are to be
avoided. In all cases, the elements are to have an aspect ratio not exceeding 3:1. Distorted elements, with
element corner angle less than 45° or greater than 135°, are to be avoided. Stiffeners inside the fine mesh zone
are to be modelled using shell elements. Stiffeners outside the fine mesh zones may be modelled using beam
elements.
Where fine mesh analysis is required for an opening, the first two layers of elements around the opening are to
be modelled with mesh size not greater than 50 mm × 50 mm. A smooth transition from the fine mesh to the
coarser mesh is to be maintained. Edge stiffeners which are welded directly to the edge of an opening are to be
modelled with shell elements. Web stiffeners close to an opening may be modelled using rod or beam elements
located at a distance of at least 50 mm from the edge of the opening.
Where fine mesh analysis is required for main bracket end connections, the fine mesh zone is to be extended
at least 10 elements in all directions from the area subject to assessment.
Face plates of openings, primary support members and associated brackets are to be modelled with at least two
elements across their width on either side.
The fine mesh models are to be based on gross scantlings reduced by tk.
The extensions of the local FE support models described below refers to the borders where tapering from coarse
global model to the 50 mm × 50 mm start. The support models shall not only cover the support itself with the
associated parts of the hull structure, but also the associated area of the cargo tank in way of the supports. This
is important to ensure that the support forces can be absorbed by the cargo tank structure without unacceptable
local stressed areas that eventually may lead to damage to the outer shell plating (the primary tank barrier).
The most critically loaded;
—
—
—
—
vertical
transverse
longitudinal
anti-floatation supports.
should generally follow the requirements below:
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.5 Local Structural Fine Mesh Analysis (ULS) – Page 31
5.3.1 Modelling of vertical supports
— Two web frame spaces is to be modelled in way of aft or forward end bulkhead in general.
— The local model should extend one web frame spacing forward and aft of the vertical support in
longitudinal direction.
— In the transverse direction, the model should in general include the neighbouring primary supporting
structures.
— Hull and cargo tank structures in way of the above supports may normally be selected with full breadth.
5.3.2 Modelling of transverse supports
For modelling of transverse supports, the transverse extension of the local model should in general be as for
the vertical supports. In longitudinal direction, the extension is required to be two web frame spaces.
— One web frame space + one web frame space where the maximum transverse reaction force is found, full
breadth.
— If different types are employed, make each model, full breadth.
— Upper and lower supports shall be modelled, full breadth.
— Hull and cargo tank structures in way of the above supports shall be modelled.
5.3.3 Modelling of longitudinal supports
— Longitudinal extension of the model may be two web frame spaces, i.e. forward and aft of the support.
— In the transverse direction, symmetry may be considered and the extension of the model should normally
be one longitudinal space from the edge of the support.
— One anti-pitch support to be modelled.
— Hull and cargo tank structures in way of the above supports shall be modelled.
5.3.4 Modelling of anti-floatation supports
— One typical support should be modelled. The model should include necessary surrounding structure and
using boundary conditions from the global model.
— Two frame space model in way of end bulkhead.
— Hull and cargo tank structures in way of the above supports shall be modelled.
5.3.5 Modelling of stiffeners subject to large lateral deformation
— Forward & aft end secondary stiffener in cargo tank, double bottom longitudinal with brackets subjected to
large deformations should be modelled.
— The stiffener model is to be extended longitudinally at least two web frame spaces from the areas under
investigation.
— The model width is to be at least 1+1 longitudinal spaces.
— The web of the longitudinal stiffener should be represented by at least 3 shell element across its depth.
— The face plate of the longitudinal stiffener and bracket should be modelled with at least two shell elements
across its width on either side.
— The prescribed displacements obtained from the cargo tank FE model should be applied to all boundary
nodes which coincide with the cargo tank model.
5.4 Load Cases
The fine mesh analysis in way of cargo tanks and tank supports is to be carried out for the load cases specified
in Table 4-2 toTable 4-3 for the locations outlined in Table 5-1. However, not all the load cases listed in Table
4-2 and Table 4-3 may be governing. The actual tank design and support configuration may vary and the
applicable load cases will have to be selected accordingly.
The fine mesh analysis of double bottom longitudinal with brackets subject to large relative deformation is to
be carried out for the load cases LC2, LC4 and LC15 in the areas specified in Figure 5-1.
5.5 Application of Loads and Boundary Conditions
Where a separate local finite element model is used for the fine mesh detailed stress analysis, the nodal
displacements from the cargo tank model are to be applied to the corresponding boundary nodes on the local
model as prescribed displacements. Alternatively, equivalent nodal forces from the cargo tank model may be
applied to the boundary nodes. The fine mesh model can also be an integral part of the cargo hold model.
Where there are nodes on the local model boundaries which are not coincident with the nodal points on the
cargo tank model, it is acceptable to impose prescribed displacements on these nodes using multi-point
constraints. The use of linear multi-point constraint equations connecting two neighbouring coincident nodes
is considered sufficient.
All local loads are to be applied to the local finite element model.
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.5 Local Structural Fine Mesh Analysis (ULS) – Page 32
5.6 Acceptance Criteria
The von Mises stress is to be calculated based on the membrane axial and shear stresses of the plate element
evaluated at the element centroid. Where shell elements are used, the stresses are to be evaluated at the mid
plane of the element (membrane stress).
It is required that the resulting von Mises stresses are not exceeding the allowable membrane values specified
in Table 5-2. These criteria apply to regions where stress concentrations occur due to irregular geometries.
Nominal stresses shall remain within the limits given in in Table 4-4.
When mesh sizes smaller than 50 mm × 50 mm is used, the average stress is to be calculated based on stresses
at the element centroid. Stress averaging is not to be carried across structural discontinuities and abutting
structure.
Table 5-2 Maximum allowable membrane stresses for fine mesh analysis
Element stress
Allowable stresses
load level
Static + Dynamic(10-8)
Static
Static + Dynamic (10-4)
Cargo tank and hull
Element not adjacent
N.A.
1.36σ F
1.09σ F
structures supporting to weld (base material)
cargo tank
Element adjacent to
N.A.
1.2σ F
0.96σ F
weld
Other hull Structures Element not adjacent
to weld (base material)
1.7σ F
1.36σ F
1.53σ F
Element adjacent to
weld
1.5σ F
1.2σ F
1.35σ F
Note:
1) The maximum allowable stresses are based on the mesh size of 50mm x 50mm. Where a smaller mesh size is used,
an average von Mises stress calculated over an area equal to the specified mesh size may be used to compare with
the permissible stresses.
2) Average von Mises stress is to be calculated based on weighted average against element areas:
n
σ von _ av =
∑ Aσ
i
von _ i
1
n
∑A
i
1
where
σ von _ av : the average von Mises stress
σ von _ i
: the von Mises stress of the i th plate element within the area considered
Ai
: the area of the i th plate element within the area considered
n
: the number of elements within the area considered
3) Stress averaging is not to be carried across structural discontinuities and abutting structure and stress values obtained
by interpolation and/or extrapolation are not to be used.
5.7 Structural verification for wood and dam plate
The detailed configuration of the wood and the dam plate should preferably be included in the local FE model
of the supports. A simplified approach is outlined in [5.7.1] and [5.7.2].
5.7.1 Strength of wood
Strength of wood should carefully be checked in view of compressive strength and shear strength Figure 5-2
shows an assumed of force transmission to wood if applied from the support. It is assumed that the reaction
force from a support will be transmitted through the top plate of the supports with angle of 90 degrees. The
compressive strength at wood can be checked as follows;
σr =
fz
Aloaded
≤
σ wood
γ SF
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.5 Local Structural Fine Mesh Analysis (ULS) – Page 33
where
fz
= load on the support normal to the support surface.
γ SF
= safety factor, 3.0 for wood
Aloaded = loaded area due to transmitted vertical force, mm2
σ wood = minimum compressive strength of wood
Loaded are due to
transmitted loads
A
Section A -A
Wood
AFFECTED AREA
o
90
Top plate of
support
A
Figure 5-2
Assumption of force transmitted
The shear strength of wood shall be checked using the transverse friction force due to the maximum vertical
force or maximum longitudinal force applied the support to be considered. Thus, the shear strength at wood
shall be satisfied as follows;
τ
f
τ r = h < wood
Aw
γ SF
where,
fh
= µ fz Friction force at support
γ SF
= safety factor, 3.0 for wood
Aw
= shear area of wood, mm2
τ wood = minimum shear strength of wood, N/mm2
5.7.2 Assessment of dam plate
Dam plate shall be fitted against the friction force and be designed with 10% of the maximum force applied to
the support to be considered, when adhesive and resin strength may be damaged. The required shear area of
dam plate is given as follows;
f
Ad ≥ h , mm
τ allow
where,
τ allow = allowable shear stress of dam plate, N/mm2
= 0 .95τ f
A small size bracket may be fitted to prevent yielding of the dam plate, if dam plate area is not sufficient.
Dam plate
Wood
fh
Bracket to support
dam plate
Resin
Top plate of
support
Figure 5-3
Force applied to dam plate
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.5 Local Structural Fine Mesh Analysis (ULS) – Page 34
Bending strength of dam plate shall also be checked with designed with 10% of the maximum force applied to
the support to be considered. Allowable stress is 0 .95σ f .
5.7.3 Material data
Material strength data shall supplied by the designer based on certification of the relevant materials.
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.6 Thermal Analysis of a Cargo Tank – Page 35
6 Thermal Analysis of a Cargo Tank
6.1 General
To determine the grade of plate and sections used in the hull structure, a temperature calculation shall be
performed for all tank types when the cargo temperature is below -10°C, Pt.5 Ch.5 Sec.2 B500 /2/.
Steady state thermal analysis of hold area and the cargo tank shall be performed for all tank types when the
cargo temperature is below -10°C (Rules Pt.5 Ch.5 Sec.2 B500) to
— determine steel temperature as basis for material quality selection of the surrounding hull structure, and
— as input to thermal stress analysis to confirm the structural integrity of the cargo tank and support system
with respect to yield and buckling in partial and full load conditions.
However, based on experience with conventional proven designs and where the cargo temperature is -55oC or
above no temperature calculations need to be carried out. See exemptions listed in Introduction in Sec.1.
Transient thermally induced loads during cooling down periods shall be considered for tanks intended for cargo
temperatures below -55 °C as required by the rules Pt.5 Ch.5 Sec.5 A901.
Thermal expansion coefficient of the material of the cargo tank is to be supplied by/documented by the
designer.
Simplified 2-D models and/or 3-D FE models may be used as applicable. If a 3-D model is deemed necessary,
the integrated cargo hold/tank finite element model used in Sec.4 may be used for the thermal stress analysis.
6.2 Thermal stress analysis
Load cases should at least be considered as follows;
— LC1: full load condition (98% filling) to determine maximum cool-down of surrounding hull structure.
— LC2: partial load condition, filling to each stringer level as relevant to determine stress ranges for low cycle
fatigue analysis for the full thermal cycle due to loading and unloading of cargo.
Thermal loads (temperature distribution loads) should be specified along the tank height for each design load
case.
For partial load conditions and full load condition, thermal load, static cargo pressure and minimum design
vapour pressure should be applied.
Deflection of double bottom structure shall be taken into account for all load conditions.
6.3 Acceptance Criteria
Allowable stress for the design load cases including thermal stress shall not exceed two times the relevant
values given in Table 4-4.
Local buckling of plates between stiffeners under thermal stress shall be checked against structural stability.
Allowable stability factors are given in the rules, Pt.5 Ch.5 Sec 5. E308.
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.7 Sloshing Assessment – Page 36
7 Sloshing Assessment
For partial tank fillings the risk of significant loads due to sloshing induced by ship motions shall be considered.
7.1 Sloshing strength analysis
The tank boundary structure shall be designed to withstand loads caused by liquid sloshing. The design sloshing
pressures are to be explicitly considered in in the scantling requirements of plates and stiffeners.
As a minimum the tank shall be designed for the sloshing inertia and impact pressure loads given in DNV Rules
Pt.3 Ch.1 Sec.4 /1/. Based on experience, this will normally be considered sufficient if swash bulkheads are
arranged to reduce liquid sloshing resonances in the tanks.
The acceptance criteria for sloshing strength analysis shall be according to the rules, Pt.3 Ch.1 Sec.4 /1/. Please
note that the rule sloshing pressures are referred to 10-4 probability level.
For tanks built without swash bulkheads and/or longitudinal bulkhead, or where the liquid motion resonance
period is found to be close to the natural motion periods of the ship (see [7.2]) the need for documentation by
more comprehensive sloshing assessments (e.g. CFD and/or model testing) will be considered by the Society
in each case.
7.2 Liquid resonance interaction
Interaction of liquid sloshing motion with the natural ship motion periods may cause violent sloshing motion
of liquids inside the tanks. Normally, the lowest natural liquid periods should be 20% away from the natural
ship motion periods to limit this effect. The fitting of swash bulkheads can move the liquid resonance periods
away from the motion periods of the ship and significantly reduce sloshing loads inside the tanks.
The natural periods for liquid motion for a prismatic tank can be approximated by, Ref. /8/;
=
2
: Natural sloshing period for mode i=1, 2, ….
where
=
=
: Natural sloshing frequency for mode i=1, 2, …..
tanh
ℎ
l = length or breath of free liquid surface at filling height h
h = filling height (distance from tank bottom to free surface)
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.8 Fatigue Analysis – Page 37
8 Fatigue Analysis
Fatigue analysis of hull structures shall be carried out in accordance with Pt.3 Ch.1 Sec.16. Unless otherwise
described, details of fatigue strength assessment are given in DNV Classification Note 30.7, Fatigue
Assessment of Ship Structures /5/.
Additional requirements may apply for the hull structure depending on class notations (i.e. PLUS, CSA).
Fatigue analysis of cargo tanks and supports is not required by the rules for conventional proven A-tank designs
where the cargo temperature is higher than -55oC (e.g. LPG/NH3 carriers), Pt.5 Ch.5 Sec.5 A 1401.
On the other hand, for novel designs, and/or when the cargo temperature is below -55oC, fatigue analyses of
the cargo tanks and the supports shall be carried out as for the hull structure, damage factor Cw ≤ 1.0.
This section describes the procedure to perform fatigue analysis of hull structures and the cargo tanks
8.1 Fatigue damage accumulation
The fatigue analysis for type A ships are based on rule loads for both the hull and the tank structure. Fatigue
stress ranges shall in most cases be determined by the use of finite element models.
The total fatigue damage may in general be obtained as follows:
where
D
ni=
Ni=
nl=
= accumulated fatigue damage ratio
number of cycles in stress block “i”
number of cycles to failure at constant stress range ∆σ
number of loading and unloading cycles covering the complete pressure and temperature range
during the lifetime of the vessel. To be taken as 103 for a trading carriers (IGC).
number of load cycles to failure for fatigue loads due to variable fillings, loading and unloading
Nj=
k
= number of stress blocks, ≥ 8
ā, m = parameters defining the fatigue S-N curve
∆σi = hot spot stress range in stress block “i”
1.0 for cargo tanks, tank supports as well as hull structure, minimum 20 years in world-wide operation
Cw≤
Guidance note:
The first term in the damage equations above can most conveniently be determined by the alternative formulation in
CN30.7 (Sec. 2) using a Gamma function
---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e---
8.2 Fatigue Damage Evaluations
The long term distributions of stresses at the critical weld locations shall be determined for the loaded, part load
and ballast conditions. The combined effect for the fatigue analysis can be determines as outlined in bullets a.
and b. below. The operational profile is defining the fraction of the total lifetime spent in the actual loading
conditions - full load, ballast, part loads and at various heading angles, Table 8-3.
The fatigue life can be determined in basically two different ways.
a) By adding up damage contributions
— Fatigue damage contributions (Miner sums) calculated for each loading condition can be added
according to the operational profile of the vessel to give the total fatigue damage contribution over the
reference lifetime of the vessel.
— For the part load condition the fatigue damage contributions from the considered filling levels can be
added according to the operating time at each filling level. A minimum of three part filling levels are
to be used.
b) By establishing a resulting long term Weibull stress distribution. This can be done by combining the long
term stress distribution for all the load cases as a weighted sum according to the operational profile for the
vessel. This reduces the number of stress cycles in each operating mode with the corresponding fractions.
Fatigue analysis on this basis is to be compared to the total design lifetime.
8.3 Locations to be checked for fatigue
The fatigue strength assessment is to be carried out for the hull, the cargo tanks, tank support structures in the
cargo area as specified in Table 8-1. Additional areas may have to be analysed based on specific structural
configurations.
DET NORSKE VERITAS AS
Classification Notes - No. 31.11, July 2013
Sec.8 Fatigue Analysis – Page 38
Table 8-1 Locations for fatigue analysis
Structure member
Structural detail
Load type
Hull structures
—
—
—
—
—
Lower hopper
—
Upper hopper
—
Cargo tank dome and Deck openings —
and coamings
—
—
Longitudinal girder connection to
—
transverse bulkhead
—
—
Top and bottom of side hold frame
—
ends
Side, bottom, inner side, — End connections of longitudinal
hopper slope and deck
stiffeners to web frames and
longitudinals.
transverse bulkheads
Hopper knuckles
—
—
Deck openings. Cargo
tank dome.
—
Double bottom longitudinal girder
—
Side hold frames
Watertight transverse
bulkheads
—
— Vertical stiffeners to inner bottom
Hull girder wave bending
Dynamic sea pressure load
Dynamic ballast pressure load
Dynamic cargo loads
Dynamic sea pressure load
Dynamic ballast pressure load
Dynamic cargo loads
Hull girder wave bending
Support deformation
Dynamic sea pressure load
Dynamic ballast pressure load
Hull girder wave bending
Dynamic cargo loads
Sea pressure loads combined with cargo and
ballast loads
— Relative deflection due to cargo loads
Cargo tank
—
—
—
—
Vertical supports
Upper & lower transverse supports
Fwd & aft end secondary stiffeners
Cargo tank, tank supHigh stressed tank structure in way of
ports,* and cargo tank in
supports
way of supports
— Bracket ends
— End connection of stiffeners
— Outer shell plate to stiffeners and
frames / girders
— Internal pressure due to:
- Vertical acceleration
- Transverse acceleration
- Longitudinal acceleration.
— Dynamic sea pressure
— Hull girder wave bending
— Sloshing (if relevant)
Cargo tank pump tower
(if used)
— Internal inertia pressure due to:
- Vertical acceleration
- Transverse acceleration
- Longitudinal acceleration.
— Sloshing forces
— General information on pump tower loads are
given in Classification Note 30.9 Sec.4 /7/.
— Tower and tower supports
— Tank dome connection
* Tank supports includes the part of the tank structure in way of supports and the support structure welded to the hull, and adjacent hull structure where
the stress mainly originates from the presence of the tank.
Note:
Several methods for fatigue analyses are available; simplified beam approach, component spectral (stochastic) analysis and full spectral (stochastic)
analysis. See CN 30.7 for details.
8.4 Finite Element Models
The determination of nominal stresses ranges for use with S-N curves and stress concentration factors can be
based on cargo hold model meshes or fine mesh analysis models dependent on the suitability for use with the
actual detail to be analysed. Alternatively, stresses can be extrapolated to the hot spot from a very fine mess (t
x t) mesh FE analysis. The extrapolation procedure is described in Classification Notes 30.7 /5/.
8.5 Calculation of stress range components
For each loading condition, local stress components due to simultaneous internal and external pressure loads
are to be combined with stress induced by dynamic hull deflections. Detailed description of the combination
of the stress components are given in Classification Notes 30.7 /5/.
The long term distribution of stress ranges may be described by a Weibull distribution. For both the hull and
the tank structure Weibull slope parameters defined by analytical expression may be used as given in CN30.7.
Unless otherwise agreed a Weibull shape parameter of 1.0 as given in the IGC code may normally be used for
the tank and tank support structure.
As the main contribution to the cumulative fatigue damage comes from the smaller waves, the long term
reference stress range should be referred to the 10-4 probability level.
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8.6 Stress processing for S-N curve fatigue analysis
Fatigue analyses shall be carried out based on the largest principal stress at the considered location.
Geometrical stress concentration factors not accounted for in the FE-model, e.g. shell thickness changes, can
be calculated according to DNV Classification Notes 30.7 and applied to the analysed stress ranges.
The principal stresses to be used in the fatigue evaluation shall be calculated as follows:
— Determine the static and dynamic combined stress for each (all) surface stress component, x, y and shear.
This shall be done at the both surfaces.
— Calculate principal dynamic stress ranges separately at both surfaces. The largest principal dynamic surface
stress range within ± 45 degrees off the perpendicular to the weld (crack) is to be used in the S-N curve
fatigue analysis.
8.7 Fatigue Strength Assessment of Hull and Cargo Tanks
For independent A-tanks ships rule loads are used for the tank system as well as the hull structure. The analyses
are to be carried out in compliance with the procedures given in Classification Notes 30.7 /5/
8.7.1 Load cases to be considered
The following load cases may be taken into account for the hull analyses.
Table 8-2 Load cases for hull fatigue strength assessment
LC
1
2
3
4
5
6
Loading Condition
Fully loaded
Fully Loaded
Ballast
Ballast
Fully loaded
Ballast
Pressure
Internal dynamic cargo pressure
External dynamic sea pressure
External dynamic sea pressure
Internal dynamic ballast load
External static pressure plus internal cargo static pressure
External static pressure plus internal ballast tank pressure
Ref.
Dynamic
Dynamic
Dynamic
Dynamic
Static
Static
Hull girder loads and loads calculated from LC1 to LC4 above shall be used for fatigue strength evaluation.
LC5 and LC6 may be used for determination of mean stress effects.
For the cargo tanks and cargo tank supports, LC 3, LC 5 and LC 6 and 7 from Table 4-2 and Table 4-3 are to
be applied for fatigue analysis of the cargo tanks and cargo tank supports.
8.7.2 Operating profile
The ship loading conditions to be used in the fatigue analysis are indicated in Table 8-2. Unless otherwise
agreed the fraction of time spent in each loading condition at sea is shown in Table 8-3 below for a normal
trading carrier (trading with full load on entire laden voyage and in ballast for return transit).
Other distributions of time fractions (exposure times) may be applied for trades that require the ship to operate
more of the time in part load conditions.
The design loading conditions and exposure times giving basis for the fatigue calculations shall be stated in the
Appendix to the Class Certificate.
Table 8-3 Design loading conditions and exposure
times, pn
IMO Type A Gas Carrier
Fully loaded condition
Ballast condition
Port
Hull structures and
support structures
0.45
0.40
0.15
8.7.3 Operation route factor for hull structure
In CN30.7, a reduction factor, fe on derived combined stress range accounting for the long- term sailing routes of
the ship. For worldwide operation the factor may be taken as 0.8. This means that for world-wide operation the
stress ranges are taken as 80% of the stress ranges obtained from North Atlantic operation. The North Atlantic
scatter diagram is given in CN30.7 and in CN30.5 Environmental Conditions and Environmental Loads.
8.7.4 Corrosion
Corrosion addition should be taken into account according to the DNV Rules /1/. The basic S-N curve for
welded regions in air is to be applied for joints situated in dry spaces or joints effectively protected against
corrosion.
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Sec.8 Fatigue Analysis – Page 40
For inner hull joints facing to cargo tanks, the S-N curve in air may normally be used.
For joints efficiently protected only a part of the design life and exposed to corrosive environment the
remaining part, the fatigue damage may be calculated as a sum of partial damages according to CN30.7.
8.7.5 Fatigue S-N Curves
The design S-N curves shall be based on mean-minus-two-standard-deviation curves (m-2s) for relevant
experimental data corresponding to 97.6% probability of survival of the S-N test data.
For the cargo tank, fatigue properties of welded material and base material used should be documented from
experiments relevant for the room temperature and the actual liquid cargo design temperature, see Table 3-1.
If relevant S-N curves for the considered material(s) are not available, the designer may need to develop such
data to the satisfaction of DNV. General procedures for development and documentation of S-N curves can be
found in CN30.7, but it is recommended that this is discussed with DNV before extensive studies are launched.
The hull structure weld joints within the scope of the assessment can be designed based on the S-N curves in
CN30.7 provided normal or high strength steel is used. The basic S-N curve for welded regions in air is to be
applied for joints situated in dry spaces or joints effectively protected against corrosion. Void cargo hold spaces
between hull and cargo tanks are normally considered as dry space.
8.7.6 Stress concentration factors
The fatigue life of a detail is governed by the hot spot stress range. The hot spot stress range is obtained by
multiplication of the nominal stress by stress concentration factors (K-factors). K-factors for the most common
details are tabulated in CN30.7. For special details (geometries) not covered by the “standard” tabulated details
in CN30.7, local very fine mesh analyses with FE meshes of size t × t, where t is the plate thickness, can be
made to determine stress concentration factors for the actual detail.
8.7.7 Mean stress effect
The stress range may be reduced dependent on whether mean cycling stress is tension or compression. This
reduction may be carried out for the base material and weld joints. The calculated dynamic stress range
obtained may be multiplied by a reduction factor fm. Details of the mean stress factor is given in CN30.7.
8.7.8 Effect of weld toe grinding
According to DNV-RP-C203 Fatigue Design of Offshore Steel Structures, the fatigue life can be improved by
grinding with a factor of 0.01 σ F (max. 3.5), where σ F = the characteristic yield strength of the material. As
corrosion of ground metal surfaces virtually eliminates the benefit of burr grinding the ground surface must be
adequately protected against corrosion.
However, toe grinding at design stage is normally not to be used if the damage factor Cw is larger than 1.47.
8.7.9 Hopper knuckle connections
The angle of hopper knuckle is one of primary design issues. A steep hopper knuckle angle is usually preferred
to minimize ballast volume and maximize the cargo volume. On the other hand, a less steep angle is preferred
in view of structure design. Thus, it is usually found that the hopper knuckle angle is between 40 and 55°.
Figure 8-1 shows an example of a fine element model with thickness size meshes.
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Sec.8 Fatigue Analysis – Page 41
Figure 8-1
A finite element model showing meshes
When a hopper knuckle angle is quite steeper and geometry of the hopper knuckle connection outside the
midship is different from than those amidships, an additional finite element model may be made.
If the required fatigue life is not satisfied, weld shape improvement is commonly used. Figure 8-2 shows details
of weld profiling. The weld bead should be ground and undercut at the weld toe removed. It should be noted
that the final grinding direction should be transverse direction in order to avoid additional notches due to the
grinding.
Figure 8-2
A design example of weld profiling
For weld toe grinding, it is required that a toe grinding depth of maximum 5% of thickness and the minimum
0.5 mm is applied according to DNV CN30.7. For thicker plates, the maximum grinding depth should not
exceed 2.0 mm. It should be noted that the final grinding direction should be transverse direction in order to
avoid additional notches due to the grinding. A burr grinder is normally used for toe grinding. Before
performing the burr grinding, the weld should be de-slagged and cleaned by a wire brush.
8.8 Fatigue assessment of cargo tank supports
The largest dynamic forces acting on supports and keying structures will be induced under full load conditions.
The dynamic forces from self-weight of cargo tanks may be negligible in ballast condition compared to the full
load condition.
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8.8.1 Locations to be checked
The following locations may be critical in view of fatigue.
—
—
—
—
—
Vertical support connection to cargo tanks and inner bottom.
Lower roll support connection to cargo tanks and inner bottom in transverse direction.
Upper roll support connection to deck transverse web in transverse direction.
Upper roll support connection to cargo tank top in transverse direction.
Pitch support to cargo tanks and inner bottom in longitudinal direction.
8.8.2 Vertical supports
Dynamic stresses in the vertical supports are caused by the following dynamic loads:
—
—
—
—
—
Horizontal acceleration,
Vertical acceleration,
Sea pressure
Double bottom bending
Hull girder bending.
The analysis procedure is:
1) Vertical loads are applied.
2) Transverse loads are applied assuming conservative static friction µ = 0.5. The tank will not be sliding for
the dominating (10-4 probability level) fatigue loads. See Figure 8-4.
3) Hull girder loads are also to be applied.
4) Correlations are applied according to CN30.7 since it is difficult to establish the correlations from the direct
analysis.
8.8.2.1 Vertical supports loaded in the transverse direction
A. Dynamic stress caused by vertical acceleration
The distribution of vertical forces may be found from the load cases in Table 4-2 and Table 4-3.
1) LC 3: fully loaded hogging condition; hull girder loads with dynamic internal (S+D) pressure and static (S)
external pressure, and
2) LC 5: fully loaded hogging condition; hull girder loads with internal static (S) pressure and external (S+D)
pressure.
Based on the calculated support forces from the mentioned load cases, the relevant stress may be calculated.
The stress range in the vertical supports shall be calculated as the difference between the stress values in LC 3
and in LC 5 after deduction of static stress from LC 1. The long term distribution of the stress is shown in Figure
8-3.
This will produce conservative results due to taking max down loads and up loads to define the stress range.
This analysis will include the effect of hull girder bending as well as double bottom bending. This will influence
on the distribution of vertical forces in the supports.
Figure 8-3
Long term distribution of stress for vertical load
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Figure 8-4
Long term distribution of transverse force on vertical supports
B. Dynamic stress caused by transverse acceleration
At a certain magnitude of the transverse acceleration the cargo tanks will slide on the vertical supports. The
probability level, Q=10-N, where the change from static to sliding friction may be calculated as
N= (µs/ at) × 8
where,
µs = 0.5 the static friction coefficient
at = is the calculated transverse acceleration as fraction of gravity (go) at probability level Q =10-8
The position where the change from static to sliding friction will occur is indicated in Figure 8-4.
The FEM calculation shall include 2 load cases specified in Table 8-4.
Table 8-4 Load cases for transverse stress calculation
Transverse acceleration, at
LC-1
Probability level Q = 10-8
Point A
Point B
Point C
LC-2
Probability level Q = 10-N
Stress to be calculated based on the
transverse force PH (= 0.5 PV)
Stress to be calculated based on the
transverse force of PH (= 0.2 PV)
Stress to be calculated based on the
transverse force of PH (= 0.2 PV)
The stress range in the supports shall be calculated considering the transverse forces to port and starboard,
Figure 8-5.
Sliding will only occur if the transverse acceleration (ay/go) is larger than the static friction coefficient, µs.
Normally, the transverse acceleration at/go will at 10-8 probability level be of the order 0.4 to 0.6. According to
the formula above sliding will then begin (point A in Figure 8-4) at 10-10 to 10-6.7 probability level. This is well
beyond the probability level of 10-4 to 10-2 where most of the fatigue damage will be accumulated. Hence, for
practical purposes, calculations can in most cases be carried out without taking sliding into account.
Figure 8-5
Load application to vertical supports (transverse direction)
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The assumption that the smaller loads are only carried by friction implies that there is no initial contact at the
transverse supports. In addition, it is assumed that the (shear) deformation of the vertical support and tank will
not cause contact.
However, based on the actual configuration, the long term distribution of loads on the transverse support should
consider the possibility of interaction (friction force and contact) also for smaller loads, taking into account
actual production tolerances and gaps.
C. Total combined stress
Combined stress from vertical acceleration and transverse acceleration is calculated as below:
2
σ comb = σ v 2 + σ trv
The calculation is to be carried out at characteristic fatigue sensitive points. The principal stress normal to, or
within ± 45o of the normal, to the weld in question shall be used as basis for the fatigue calculation, Ref. CN30.7
Sec. 2.3.
8.8.2.2 Structure loaded in the longitudinal direction
When considering the longitudinal direction in addition to longitudinal acceleration, hull girder bending and
double bottom bending need to be considered in order to determine the actual number of vertical supports in
contact with the tank.
A. Stresses caused by vertical acceleration
To be calculated as described in [8.8.2.1] A. This analysis shall include the effects of vertical acceleration,
double bottom bending and hull girder bending.
B. Dynamic stress caused by longitudinal acceleration
The vertical support force may be taken from the static load condition. The typical longitudinal acceleration is
in the range of 0.15 ~ 0.2g. With a static friction coefficient is 0.5 no sliding is expected for this load condition.
The stress amplitude may be calculated based on the load application shown in Figure 8-6.
Plong = (Pw ⋅ a x ) / n
where, Pw = static cargo weight
ax = longitudinal acceleration
n = number of active vertical supports allowing for
the deformation of the double bottom.
Figure 8-6
Load application to vertical supports (longitudinal direction)
Figure 8-7
Long term distribution of stress for longitudinal load
The long term distribution of the stress is shown in Figure 8-7.
C. Hull girder bending
The hull girder bending causes elongation of the inner bottom. The cargo tank is in most cases rather stiff and
will resist the imposed elongation from the inner bottom. Thus, it will create longitudinal forces in the vertical
supports. The flexibility at/in the vertical supports will have effect on the longitudinal forces occurring in the
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Classification Notes - No. 31.11, July 2013
Sec.8 Fatigue Analysis – Page 45
vertical supports. In order to take into account the flexibility of the supports, calculations may have to be carried
out. The flexibility will have effect on at which level of the hull girder moment sliding will occur.
D. Total combined stress
The combined stress from vertical acceleration and double bottom bending (σv), longitudinal acceleration
(σlong) and hull girder bending may be calculated by using the formula below:
σ comb = σ v 2 + (σ long + σ hull _ bending )2
The calculation is to be carried out at characteristic fatigue sensitive points. The principal stress normal to, or
within ± 45o of the normal, to the weld in question shall be used as basis for the fatigue calculation, Ref. CN30.7
Sec. 2.3.
8.8.3 Transverse supports
Dynamic stresses in the transverse supports are caused by transverse acceleration.
The load for the roll supports are based on the max. transverse acceleration load cases LC 6-7 in Table 4-2 and
Table 4-3.
The total transverse forces acting on the cargo tanks will be supported by upper and lower transverse supports
and friction forces in the vertical supports. The distribution of the supporting forces between friction force in
the vertical supports and the transverse supports will vary depending on the magnitude of the transverse
dynamic force (transverse acceleration) and the actual gaps at the transverse supports. The analysis shall be
carried out using an iterative procedure as described in [4.1.7.2].
The following assumptions are made:
1) With small transverse accelerations, the transverse load from the cargo tank will be carried by static friction
in the vertical supports only.
2) With larger transverse acceleration, the transverse cargo tank load will be carried partly by friction in
vertical supports and partly by forces in the transverse supports.
3) The friction coefficient used should be considered based on a low value for the dynamic friction coefficient
that shall not exceed µ=0.2, unless otherwise documented by the designer
The sum of the friction force in the vertical supports which may be taken into account shall not exceed:
Pfriction = Pw × µd
where,
Pw = static cargo and tank weight.
µd = 0.2 : lower bound for sliding friction coefficient
The long term distribution of stress is shown in Figure 8-8. “A” is drawn based on calculated stress, σ1, from
a transverse load where no friction force is included. The effect of the friction in the vertical supports is that
the transverse supports will not be loaded for small values of the transverse acceleration. This calculated
friction force, Pfriction, will cause a stress which is equivalent to σ2. Thus, transverse accelerations causing a
stress less than σ2 will not cause stress in the transverse supports and the area marked, B, can be removed from
the fatigue load diagram.
Thus, the effective fatigue load diagram to be used in the fatigue calculations is shown in Figure 8-9. The stress
range shall be used in the fatigue analysis.
Figure 8-8
Long term distribution of stress
Fig. 8.8 Long term distribution of
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Sec.8 Fatigue Analysis – Page 46
Figure 8-9
Effective fatigue load diagram
Fig. 8.8 Long term distribution of
Fig. 8.9 Effective fatigue load
The details of the procedure used in the fatigue analysis are shown in Table 8-5.
Table 8-5 Procedure used in the fatigue calculation
Long term stress
distribution
Mean stress effect
Fraction of time at
sea
S-N curves
— Long term stress range distribution determined from rule loads and structural stress analysis
with FE models using a Weibull slope parameter of h=1.
— Total number of cycles to be calculated considering the effect of friction in the vertical
supports
— Stress range based on 10-4 probability level as illustrated in Figure 8-9.
— σ1 are σ2 are extracted directly from a fine mesh (t x t) analysis and linear extrapolation is done
to get hot spot stresses. See CN 30.7 for extrapolation procedure
See CN 30.7 Sec 2.3.4 for mean stress effect.
— Fraction factor of 0.45 is used for the life time operating under full load condition
— Stresses from ballast condition is assumed to be negligible
— S-N curves defined by parameters given in Classification Note 30.7 Table 2-1 or 2-2 can be
used as appropriate.
8.8.4 Longitudinal supports
The longitudinal support is not included in the fatigue calculations as the longitudinal acceleration is relatively
small in normal ship operation and the longitudinal load is absorbed by the friction in the vertical supports.
8.8.5 Anti-floatation supports
The anti-flotation supports are supports designed to prevent the tank in an accidental cargo hold flooding
situation to float up and need therefore not be subject to fatigue calculations (ALS situation).
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Sec.9 References – Page 47
9 References
/1/
DNV: Rules for Classification of Ships, Pt. 3 Ch.1 Hull Structural Design, Ships with Length 100 metres
and above.
/2/ DNV: Rules for Classification of Ships, Pt.5 Ch.5 Liquefied Gas Carriers.
/3/ The International Code for the Construction and Equipment of Ships Carrying Liquefied Gases in Bulk,
IGC Code. Res. MSC.5(48), with the following amendments; Res. MSC.30(61) (1992), Res.
MSC.32(63) (1994), Res. MSC.59(67) (1996) and Res. MSC.103(73) (2000).
/4/ USCG: Safety Standards for self-propelled Vessels carrying Bulk Liquefied Gases, 46 CFR (Code of
Federal Register), Part 154, § 154.172/178.
/5/ DNV: Classification Notes No. 30.7 Fatigue Assessment of Ship Structures.
/6/ DNV: Recommended Practice, DNV-RP-C201, Buckling Strength of Plated Structures.
/7/ DNV: Classification Notes No. 30.9, Sloshing Analysisi of LNG Membrane Tanks.
/8/ Faltinsen, O. M. and Timokha, A. N: Sloshing, Cambridge University Press, 2009.
/9/ DNV: Classification Notes No. 31.13, Strength Analysis of Independent Type C Tanks.
/10/ IACS: Common Structural Rule for Oil Tankers and Bulk Carriers, External release, April 2013.
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